Edit : Consider giving a reason for down vote.

In my research, I have come across a this paper from the Computational Geometry field and I am not able to understand the concept of Maximal-Rectilinear Convex Hull (or mr-convex hull) is given on page 160, Def 2.4 of the linked paper. In the attached image I have tried to explain my problem. Please read the image in the numeric sequence of 1 to 4 to understand my question.

Appreciate any help in clearing my confusion.